Pythagorean theorem

1. Objective
The student will be able to:
use the Pythagorean Theorem
Designed by Skip Tyler, Varina High School

2. What is a right triangle?
It is a triangle which has an angle that is 90
degrees.
The two sides that make up the right angle
are called legs.
The side opposite the right angle is the
hypotenuse.
leg
leg
hypotenuse
right angle

3. The Pythagorean Theorem
In a right triangle, if a and b are the
measures of the legs and c is the
hypotenuse, then
a2 + b2 = c2.
Note: The hypotenuse, c, is always
the longest side.

4. Find the length of the
hypotenuse if
1. a = 12 and b = 16.
122 + 162 = c2
144 + 256 = c2
400 = c2
Take the square root of both sides.
20 = c
2
400 c


5. 52 + 72 = c2
25 + 49 = c2
74 = c2
Take the square root of both sides.
8.60 = c
Find the length of the hypotenuse if
2. a = 5 and b = 7.
2
74 c


6. Find the length of the hypotenuse
given a = 6 and b = 12
1. 180
2. 324
3. 13.42
4. 18

7. Find the length of the leg, to the
nearest hundredth, if
3. a = 4 and c = 10.
42 + b2 = 102
16 + b2 = 100
Solve for b.
16 - 16 + b2 = 100 - 16
b2 = 84
b = 9.17
2
84
b 

8. Find the length of the leg, to the
nearest hundredth, if
4. c = 10 and b = 7.
a2 + 72 = 102
a2 + 49 = 100
Solve for a.
a2 = 100 - 49
a2 = 51
a = 7.14
2
51
a 

9. Find the length of the missing side
given a = 4 and c = 5
1. 1
2. 3
3. 6.4
4. 9

10. 5. The measures of three sides of a triangle
are given below. Determine whether each
triangle is a right triangle.
, 3, and 8
Which side is the biggest?
The square root of 73 (= 8.5)! This must be
the hypotenuse (c).
Plug your information into the Pythagorean
Theorem. It doesn’t matter which number
is a or b.
73

11. 9 + 64 = 73
73 = 73
Since this is true, the triangle is a
right triangle!! If it was not true, it
would not be a right triangle.
Sides: , 3, and 8
32 + 82 = ( ) 2
73
73

12. Determine whether the triangle is a right
triangle given the sides 6, 9, and 45
1. Yes
2. No
3. Purple